Fix invitation flow error by adding SessionProvider

- Add SessionProvider to root Providers for NextAuth React hooks
- Add error handling to auth layout to prevent crashes on auth check failure
- Add MENTOR role redirect in auth layout

Co-Authored-By: Claude Opus 4.5 <noreply@anthropic.com>

src/app/providers.tsx

@@ -1,6 +1,7 @@
 'use client'
 
 import { useState } from 'react'
+import { SessionProvider } from 'next-auth/react'
 import { QueryClient, QueryClientProvider } from '@tanstack/react-query'
 import { httpBatchLink } from '@trpc/client'
 import superjson from 'superjson'
@@ -51,8 +52,10 @@ export function Providers({ children }: { children: React.ReactNode }) {
   )
 
   return (
-    <trpc.Provider client={trpcClient} queryClient={queryClient}>
-      <QueryClientProvider client={queryClient}>{children}</QueryClientProvider>
-    </trpc.Provider>
+    <SessionProvider>
+      <trpc.Provider client={trpcClient} queryClient={queryClient}>
+        <QueryClientProvider client={queryClient}>{children}</QueryClientProvider>
+      </trpc.Provider>
+    </SessionProvider>
   )
 }